This paper is a review of earlier results mostly described in [1]}, [2]}, [3]}, [4]}, [5]}. In particular, the check-operators (see examples in Sections REF  and REF  below) were introduced in [1]}, [2]}, where their properties were discussed. Among the check-operators, there is the main check-operator (see Section REF ) with the crucial property (REF ). In a different situation, this main check-operator was discussed in [5]}.
